In this paper we present results for the wave-vector dependent shear viscosity for a model atomic fluid with short ranged repulsive interactions computed by molecular dynamics simulations. It is shown that the data can be fitted to two different simple functional forms over a large density range, namely, a function composed of two Gaussian terms and a Lorentzian type function with a variable wave-vector exponent. The parameters of both functional forms are found to obey simple density dependencies. While the first functional form has the advantage that the inverse Fourier transform can be found analytically, the Lorentzian type function fits the wave-vector dependence better over the range of wave vectors and densities studied here. The results show that the real space viscosity kernel has a width of 2 to 3 atomic diameters. This means that the generalized hydrodynamic constitutive relation is required if the strain rate varies significantly over this distance, a situation commonly encountered for nanofluidic flows.